Elliptic Curve Cryptosystems-Based Date-Constrained Hierarchical Key Management Scheme in Internet of Things

Sensors and Materials, Vol. 31, No. 2 (2019) 355–364 355 MYU Tokyo S & M 1776 Elliptic Curve Cryptosystems-based Date-constrained Hierarchical Key Management Scheme in Internet of Things Tsung-Chih Hsiao,1 Tzer-Long Chen,2 Tzer-Shyong Chen,3* and Yu-Fang Chung4 1School of Arts, Southeast University, Nanjing 211189, China 2Department of Information Technology, Ling Tung University, Taichung 40852, Taiwan 3Department of Information Management, Tunghai University, Taichung 40704, Taiwan 4Department of Electrical Engineering, Tunghai University, Taichung 40704, Taiwan (Received May 23, 2018; accepted October 18, 2018) Keywords: mobile agent, mobile security, Internet of Things, key management, date-constrained In this paper, we propose a new mechanism to improve the disadvantage of the security mechanism proposed by a scholar and then fulfill the demands of Internet of Things (IoT) to go through the decentralized environment access control functions. We also propose the date-constrained hierarchical key management scheme for mobile agents. With elliptic curve cryptosystems (ECCs) and discrete logarithms, the proposed scheme is flexible. Moreover, the duration of access for each security class is restricted with a certain authorized discrete time period. We demonstrate the mathematical derivation and arguments for our scheme and further conduct a numerical trial. The constructed scheme could meet security needs and be more space-efficient. 1. Introduction Owing to the advantages of elliptic curve cryptosystems (ECCs), the scheme can recognize an access control object faster with a small key storage space. In this study, the scheme was constructed to reduce the work of key management, minimize key storage, enhance the computation time of construction and derivation phrases, and provide high flexibility and security. An ECC was proposed by Koblitz(1) and Miller(2) in 1985. To improve the existing cryptosystems,(3) the proposed ECC was used to reduce system parameters, public key certificates, bandwidth usage, power consumption, and hardware processor requirement, and for rapid implementation. Thus, the ECC with its advantages is useful for building a cryptosystem with high security and efficiency.(4) The mathematical illustration is described below.(4,5) Elliptic curves are categorized into two families: prime and binary curves. Prime curves (Zp) are suitable for use in software applications since they do not need to be extended for bit- fiddling operations. On the other hand, binary curves [GF(2n)] are for hardware applications since they need a small number of logic gates to build a cryptosystem. With the property of elliptic curves, the efficiency of ECC computing operation increases. *Corresponding author: e-mail: [email protected] https://doi.org/10.18494/SAM.2019.2085 ISSN 0914-4935 © MYU K.K. https://myukk.org/ 356 Sensors and Materials, Vol. 31, No. 2 (2019) 2. Previous Work In 1998, Volker and Mehrdad(5) designed a tree-structure-based security scheme of securing a safer place for mobile agents. The functions of this mechanism are distinguished into three categories: mobile agent authorization, key management, and access control. Thus far, Jeng and Wang,(6) Chung et al.,(7) Nikooghadam et al.,(8) and Lin and Hsu(9) have contributed to the incipience of a reliable and effective scheme for mobile agents. In 2006, Jeng and Wang(6) applied an ECC as a key management scheme to efficiently solve hierarchical access control problems. In the key derivation phase, a predecessor accesses the authorized files to derive encryption/decryption keys. We can use not only a secret key that is private to itself, but also the successor-related public information. Nevertheless, the scheme proposed by Jeng and Wang(6) had a loophole in security, which makes it possible for any outsider to derive an unauthorized encryption key. The relationship between any security classes was updated. The scheme proposed by Lin and Hsu(9) indicated such a flaw in the Jen (6) and Wang scheme by suggesting that an adversary could further derive the encryption key kj,2 of the security class kj,2 = fj(vl,j) without knowing any secret information. In 2008, another key management scheme was introduced by Chung et al.(7) This key management scheme was a novel and efficient solution to the dynamic access control problems in a user hierarchy by means of ECCs and one-way hash functions. The scheme introduced by Chung et al.(7) was different from that of Jen et al. in the application of polynomials. In Jen et al.’s scheme, each security class selected its own secret key and then sent the secret key to the Certificate Authority (CA) via a secure way, whereas in Chung et al.’s scheme, the same public polynomials were used in key generation and derivation phases. The CA was responsible for selecting all the secret parameters and sending them to the corresponding security classes via a secure way. On the other hand, constructing the interpolating polynomials requires both tremendous storage accommodation and a colossal amount of computational overhead. According to Knuth,(10) the cost of constructing an interpolating polynomial of degree m is derived by m additions, 2m2 + 2 subtractions, 2m2 + m − 1 multiplications, and m + 1 divisions. With respect to expenditure, Chung et al.’s scheme requires large computational expenditures and this suggests the considerable consumption of system resources to access confidential files. Hence, Nikooghadam et al.(8) introduced an ECC-based improved method for access control and key management. In 2009 and 2011, an improved version was raised by Jeng et al.’s scheme. They replaced (Ã(njPi)),Ki), which was proposed in Jeng et al.’s scheme with (h(r || Ã(njPi)),Ki) using a random number, r, and the one-way hash function h(·). This equation implies that Ã(njPi) is not a solution of fxii()−= fx () 0 anymore. The preference for this method over Jen et al.’s scheme is due to the fact that it can effectively eliminate the security flaw mentioned above. The elliptic curve discrete logarithm problem (ECDLP) is significantly more difficult and has a larger computational complexity than the integer factorization or discrete logarithm problem.(11) To satisfy security requirements, the ECC needs a comparatively smaller key size than the other cryptosystems. ECC-based access control schemes enjoy high security performance at the expense of bulky mobile agent codes and excessive calculations for encryption/decryption keys. Sensors and Materials, Vol. 31, No. 2 (2019) 357 This mechanism based on the ECC theory, therefore, is more efficient and less computationally complex with respect to key generation and derivation. Compared with the other published schemes, in addition to using elliptic curve cryptography, our scheme also incorporates the concepts of elliptic curve digital signature and data constraint. The purpose of using the concept of elliptic curve digital signature is to ensure that a private key is generated for a user only at a legal time granule as a data-bound warrant. The purpose of using the Internet of Things (IoT) is to be able to share resources and information. IoT, itself, provides an open and public manipulation environment. The heterogeneity of data enables the management and sharing of resources and information. However, ensuring the confidentiality, correctness, and availability of the legally stored information definitely becomes a challenge for sharing information from the past to the present. Since the environment of the internet is unpredictable, this often leads to security problems, such as unauthorized access requirements, data being compromised or unauthorized access, and privacy disclosure; these issues can reveal the necessity and importance of the access control mechanism. Simultaneously, based on some scholars, Volker and Mehrdad(5) suggested some methods of access control to the acting agent and key management mechanism. These will consume the agent’s time and cause security problems. When the application of mobile agents roams the internet, it may be attacked by unfriendly agents or the host or the agents will arrive at an unfamiliar or unknown host. This situation will lead to tampering or inaccurate execution of delivered tasks, resulting in private information being peeped or stolen. In this paper, therefore, an access control mechanism is proposed. The application of a mobile agent who is in a hierarchical relationship structure can adequately use the one-way hash function, the concept of time series, and ECC to ensure the security of the key; simultaneously, it can give the permission classification in order to achieve security. 3. Proposed Scheme Akl and Taylor’s proposed access control scheme(12) was based on a hierarchical structure model, which was obtained by assigning each user to a security class, which can be represented as SC = {SC1, SC2, SC3, …, SCk}. On the basis of the hierarchical structure, the access relationship between one security class and another can be denoted by SCi ≥ SCj. For instance, the class of SCi is at a higher hierarchy than SCj and their relational representation is SCi ≥ SCj. The higher the hierarchy, the more authority to access the information. This means that the user SCi has the authority to access the information available to SCj. As the hierarchy network grows, SCi would have to accommodate a growing number of private keys held by groups at a lower hierarchy. It is considered that a lower hierarchy would cause key management problems and security issues. Thus, Akl and Taylor raised the concept of superkey in place of key. In this manner, key management issues can be resolved. On the basis of the determined hierarchical structure of SCi ≥ SCj, the user SCi uses mathematical operations to obtain the SCj’s superkey with his superkey. Figure 1 shows an illustration of an improved version of Akl and Taylor’s structure. Among the leaf nodes of a hierarchical structure, we shall offer an explanation regarding the access of 358 Sensors and Materials, Vol.

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